We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.

If error is corrected whenever it is recognized as such, the path of error is the path of truth.

We must... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.

Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.

The statement that although the past can be recorded, the future cannot, is translatable into the statistical statement: Isolated states of order are always postinteraction states, never preinteraction states.

We can... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics.

Philosophy is regarded by many as inseparable from speculation. ... Philosophy has proceeded from speculation to science.